Sequential Coherent Optical Reconstruction from Projections Using a Roach Filter

Abstract

A sequential optical technique of reconstruction of a cross-sectional tomographic plane of a 3-D object, from its projections, is presented. The data are preprocessed by means of a technique for coding image information in real time and an analogical inversion of the equation of convolution, involved in the theory, is achieved with a synthetic holographic filter (R.O.A.C.H.). The principle of the method is derived from the properties of linearity of the mathematical operations used in computerized transaxial tomography. The order of the operations may be inverted and the treatment be performed sequentially by using one-dimensional filters or grids in a simple coherent optical processor. The method may be used to measure a local parameter of a 3-D pbject, relatively transparent to electromagnetic energy, such as a coefficient of attenuation in X.R. Tomography or phase variations in biological objects. To reconstruct 3-D refractive index or phase profiles we have designed an optical interferometric set-up to record the “projections”.